Hi all,

I compiled Niels', Jeroen's and my comments and will paste this into CDS if I get no more comments before 2:

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Dear Tom, Nicola and friends,

Congratulations for that impressive result. We are getting close to the roadmap (the central values as well, unfortunately...) Here are the comments from the Nikhef group.

A few general comments:

It's a difficult analysis resulting in a difficult paper to understand and more so to write. You've done a great job but there are still some places that could be clarified, especially Section 7.

We find the description of the phi folding a bit detailed for the introduction. We suggest to be more brief in the intro, and move more detail to Sec.7.1.

Fig.2: There seems to be a hump in all 6 bins around 5600 MeV. That happens to be the end of your training window. Have you studied these events?

Table 2: It's not clear to use why you need to give corrected and uncorrected numbers. They are consistent at the 1/10th of a sigma level. Why not just give a systematic?

Eq.(7) is a bit vague. We wouldn't know where to plug in these terms. Why is there an or? Either say more or less.

372: phimumu is on the same timescale as your paper. You could refer to it (here I'm getting myself into trouble as I just recommended to Christoph to refer to your paper - PK). But can't these decays be trivially vetoed at no signal cost. The phi is so narrow it cannot eat into the K* signal.

Some maths questions and comments: L. 17 / Eqs. 1+2: - Both sin(phi) and the sign of cos(phi) are needed to determine phi. - Is this the correct definition of sin(phi)? - sin(phi) = [ (p^_mu+ x p^_mu-) x (p^_K+ x p^_pi-) ] . p^_K* - cos(phi) = (p^_mu+ x p^_mu-) . (p^_K+ x p^_pi-) * L. 17 / Eqs. 1+2:

Eq. 3: S_6 * cos^2(t_K) * cos(t_l) --> S_6 * sin^2(t_K) * cos(t_l) (cos^2(t_K) is for the longitudinal--scalar interference)

L. 249: From the expressions of observables in terms of amplitudes, one would (naively) expect the boundaries of A_FB and A_9 to be: |A_FB| <= 3/2 * (1-F_L) and |A_9| <= 1 * (1-F_L) (without taking into account correlations between A_FB, A_9 and S_3). Where does the factor two difference come from?

L. 29, 33, 36, 308, 309, 398, 500, Tab. 2, Fig. 4: "K* amplitudes"/"K* polarisations": This is a bit sloppy. In general, the K* polarization doesn't fully determine the state of the mumuK* system. For example, it is also longitudinal for the state in which the mumu polarization is timelike. Maybe "decay amplitudes" and "polarization states"?

Sect. 7.3, App. A: It is not obvious how the q^2-dependent factors in Eqs. 7, 14 and 15 are obtained. The most general expressions for the observables in terms of amplitudes cannot be written in this form. Can you indicate which assumptions for form factors and Wilson coefficients were made to obtain the large-recoil dilution factors? Is it described somewhere how this was done?

L. 400-408: It is not entirely clear how F_S can be determined with the measurements of A_S: - You explain the procedure for "the P-wave amplitude" and "the S-wave amplitude". For single (transversity) amplitudes one can see how the magnitude of the S-wave amplitude can be determined from the difference in this 0-S interference term above and below the resonance. However, it is not obvious that this works if all observables are sums of left- and right-handed and B and Bbar terms. Do you need to make assumptions here? - Are values for F_L needed for this estimate of F_S? How are these obtained? - Do you combine this estimate of F_S with the direct measurement from the F_S term in the differential decay rate?

460: As you claim the zero-crossing point is precisely known, can't we include a prediction with error?

Purely textual comments:

Abstract+L.457 [no brackets around result] 7: [specify: ] '... larger theoretical uncertainties form hadronic form factors.' 10: why "so"? 17: and 19: no colon Eq.(1) and (2) replace . by \cdot 22: use \CP everywhere 23: of the one for the B0 decay (it's the definition, not the B that is transformed) 26: corresponds to -> is (?) 34: 3*S_2^s = 1-F_L --> 4*S_2^s = 1-F_L 34: S_6 is responsible for generating... S_6 and A_FB are just different parametrisation of the same thing. Please reword. e.g. Add the conversion factor between AFB and S6. 37: "not suppressed... involved". As opposed to what? 46: and _to_ provide (increases readability) 47: why don't you give the angular expression here? Isn't it equation 6? At least forward reference it. 49: {\rm Re} (we think) 50: [skip the colloquial sentence: ] 'Hence they are .. cleaner.' 56: Sections 4 and 5 are not mentioned. The backgrounds are in Section 4, not 3. 58: ', in terms of cos theta_l, ... ' 62: why [6] and not [44]? 71: do you need two citations of [10]? 90: which primary? 91: replace [18] by trigger paper [11]. 100: remove "consistent with that of the K*(892)" 122-123 [add commas:] ', and populates ... mass range, ' 133 'Psi(2S) mesons.' 136: "... are shown in Fig.~1." (not for reference) 146: Use template \Lb and \L. 148-151: rewrite that in 2 sentences. 149 'picking up' -> 'using' 153: and many other places. Why not J/psiK* instead of K*J/psi? It is much more common. 153: and a muon as a pion or a kaon (people outside LHCb do not know any track is a good pion). 156 Ref.[21] is old. Should be: arXiv:1301.5286] 157: [Why Yukawa??] 'SM Yukawa couplings' -> 'CKM elements' 160: SM simulation sounds like you're simulating the whole Standard Model. 162: the geometry cannot bias a distribution. Its acceptance does. 170: the K*0 decay. 176: What do you mean with 'normalised' and 'have the correct statistical power' ? 179: 2.0 -> two. 188: principle -> principal? 193: Is that really two CB or is one reversed? Fig.2 [x-axis more clear if:] m_Kpimumu -> m(Kpimumu) SetTitle("#font[12]{m}(K^{+}#pi^{#font[122]{-}}#mu^{+}#mu^{#font[122]{-}}) [MeV/#font[12]{c}^{2}]") Caption Table 1: Maybe mention what the second (and first) uncertainty is? 209 [don't repeat decay decsriptors] 'The values for the branching fractions are BR(.... ' 210: you should explain here why you use [24] and not [22] for J/psiK* 223 and 226: / -> and (or or) 251: "have an immediate correspondence to the transformations" rephrase 255: helicity _or_ transversity. BTW are they defined? If these relationships are not reproduced where, where can we find them? 256 and elsewhere: why put A^Re_T and A_T^2 in parentheses? You measure all of those. 260: uni-angular sounds like jargon. 261-264: How is the wrong-ID probability parameter omega treated in the fit? Is it fixed/constrained to the MC number from Section 4? 265: signal -> angular distribution, or model, or... 267: The angular observables vary... This is very important and should be mentioned the first time you explain you do fits in bins. 269: (1-F_L) why the parenthesis? 275 and 287: Feldman-Cousins 283: express? exhibit? 286: 'row' -> 'column' 302: We had to think a bit to realise that largest recoil was the lowest q^2 bin. Why not call it like that? 305: "dilute the impact of the observables" is also very vague. Footnote 2: Ref [31] is not the same as the gamma combination paper uses for the same method. We have no opinion on who's right, but one should agree if possible. 309 [missing 'meson' and 'be'; skip 'only one'; rewrite:] 'K*0 meson, FL, turns out to be the only observable that' L.310/311 [unclear, how about:] 'sensitivity to FL arises mainly from the shape of the costheta_k distribution, ' Fig.4 S_3 is bound to be less than 1/2(1-F_L). You could zoom in to at least -0.5<S_3<0.5. [caption] : 'prediction is included' -> 'prediction is shown' 316: S_3/A_FB : S_3 and A_FB. Or are you making a fraction? 333: SM _prediction_ 343: Can't you test the assumption of equal B and Bbar in your sample? 350: faithfully reproduce -> are in agreement with 369: You neglect 0.25? That should be explained. 421: A large sample. Not all? 424: by 7% -> by up to 7%

Eq.12 would look better with: \left(1-F_{\rm L}(q^2)\right) [7] BELLE -> Belle [11] LHCb. There's an arxiv number. [18] Still needed? [21] There seems to be a space missing before TeV (to be replaced anyway)

Cheers,

Patrick, Jeroen, Niels for the Nikhef group